Tunable transmittance in anisotropic two-dimensional materials

A uniaxial strain applied to graphenelike materials moves the Dirac nodes along the boundary of the Brillouin zone. An extreme case is the merging of the Dirac node positions to a single degenerate spectral node, which gives rise to a new topological phase. Then isotropic Dirac nodes are replaced by a node with a linear behavior in one and a parabolic behavior in the other direction. This anisotropy influences substantially the optical properties. We propose a method to determine characteristic spectral and transport properties in black phosphorus layers, which were recently studied by several groups with angle-resolved photoemission spectroscopy, and discuss how the transmittance, the reflectance, and the optical absorption of this material can be tuned. In particular, we demonstrate that the transmittance of linearly polarized incident light varies from nearly 0% to almost 100% in the microwave and far-infrared regime.

Figure 1

Left: Generic hexagonal lattice. The isotropic case is characterized by all equal hopping integrals $t_j^{}$. This isotropy is lifted once $t_j^{}$ become different. Right: Real and imaginary part of conductivity components. The number $t\sim 2.8\mathrm{eV}$ refers to the hopping parameter of the isotropic graphene. The cutoff energy is chosen at the position of the Van Hove singularity in isotropic graphene, i.e., ${\epsilon }_c^{}=2t$.

Figure 2

Left: Transmittance as function of the incident polarization angle for different light frequencies measured in units of the hopping energy $t$. Right: Reflectance as function of the incident polarization angle for different light frequencies measured in units of the hopping energy $t$.

Figure 3

Left: Absorption as function of the incident polarization angle for different light frequencies measured in units of the hopping energy $t$. Close to 0 and $\pi$, there are narrow regions where the absorption is approximately constant. Right: Absorption as function of the light frequency for different polarization angles.